This is an announcement for the paper "Approximation of operators in Banach spaces" by Oleg I. Reinov.

Abstract: It is a translation of an old paper of mine. We describe the topology tau_p in the space Pi_p(Y,X), for which the closures of convex sets in tau_p and in *-weak topology of the space Pi_p(Y,X) are coincident. Thereafter, we investigate some properties of the space Pi_p, related to this new topology. 2010-remark: Occasionally, the topology is coincides with the lambda_p-topology from the paper "Compact operators which factor through subspaces of l_p", Math. Nachr. 281(2008), 412-423 by Deba Prasad Sinha and Anil Kumar Karn.

Archive classification: math.FA

Mathematics Subject Classification: 46B28

Citation: In the collection "Primenenie funkcional'nogo analiza v teorii

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http://front.math.ucdavis.edu/1002.3902

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http://arXiv.org/abs/1002.3902

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